Read the given passage and select the correct option for the following questions. The sound returning back towards the source after suffering reflection from a distant obstacle like wall, hill etc. is called an echo. A cracker is fired by a child. The child hears an echo from a cliff 4 seconds after the sound produced by a cracker. The speed of sound in air at `20^(@)C` is 344 `ms^(-1)`.
What is the minimum distance between the observer and the obstacle for echo to be heard?

Options

A. 17.2 m
B. 15.2m
C. 14.2 m
D. 34.4 m

Explanation

To find the minimum distance between the observer and the obstacle for the echo to be heard, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Echo**:
An echo is the sound that is reflected off a surface and returns to the listener. The time taken for the sound to travel to the obstacle and back to the observer is crucial for calculating the distance.

2. **Identify Given Data**:
- Time taken to hear the echo (T) = 4 seconds
- Speed of sound in air (v) = 344 m/s

3. **Calculate the Total Distance Traveled by Sound**:
The sound travels to the obstacle and then back to the observer. Therefore, the total distance (D_total) traveled by the sound is given by:
\[ D_{total} = v \times T \]
Substituting the values:
\[ D_{total} = 344 \, \text{m/s} \times 4 \, \text{s} = 1376 \, \text{m} \]

4. **Calculate the Minimum Distance to the Obstacle**:
Since the total distance is the distance to the obstacle and back, the minimum distance (D_min) to the obstacle is half of the total distance:
\[ D_{min} = \frac{D_{total}}{2} = \frac{1376 \, \text{m}}{2} = 688 \, \text{m} \]

5. **Conclusion**:
The minimum distance between the observer and the obstacle for the echo to be heard is **688 meters**.